In this paper, we delve into a nuanced aspect of the distillability problem within the realm of entanglement theory, specifically examining the distillability of anti-diagonal [Formula: see text] entangled Werner states under the framework of local operations and classical communication (LOCC). To address this, we scrutinize a conjecture central to the distillability issue, initially focusing on its implications in 4-dimensional and 5-dimensional contexts. Through rigorous calculations, we establish that these cases align with the conjecture. Subsequently, we broaden our investigation to encompass [Formula: see text] matrices, demonstrating that both even and odd n-dimensional anti-diagonal matrices are in concordance with the conjecture, thus contributing to a deeper understanding of the distillability problem in quantum entanglement.In this paper, we delve into a nuanced aspect of the distillability problem within the realm of entanglement theory, specifically examining the distillability of anti-diagonal [Formula: see text] entangled Werner states under the framework of local operations and classical communication (LOCC). To address this, we scrutinize a conjecture central to the distillability issue, initially focusing on its implications in 4-dimensional and 5-dimensional contexts. Through rigorous calculations, we establish that these cases align with the conjecture. Subsequently, we broaden our investigation to encompass [Formula: see text] matrices, demonstrating that both even and odd n-dimensional anti-diagonal matrices are in concordance with the conjecture, thus contributing to a deeper understanding of the distillability problem in quantum entanglement.

Modern Physics Letters BJan 29, 20241 citation

More on quantum entanglement

F.J. Duarte

Institute of Physics eBooksOct 1, 20190 citations

A matrix inequality related to the entanglement distillation problem

Lilong Qian, Lin Chen, Delin Chu +1 more

The pure entangled state is of vital importance in the field of quantum information. The process of asymptotically extracting pure entangled states from many copies of mixed states via local operations and classical communication is called entanglement distillation. The entanglement distillability problem, which is a long-standing open problem, asks whether such process exists. The 2-copy undistillability of $4\times4$ undistillable Werner states has been reduced to the validness of the a matrix inequality, that is, the sum of the squares of the largest two singular values of matrix $A\otimes I + I \otimes B$ does not exceed $(3d-4)/d^2$ with $A,B$ traceless $d\times d$ matrices and $||A||_F^2+||B||_F^2=1/d$ when $d=4$ . The latest progress, made by Ł.~Pankowski~ et al~[IEEE Trans. Inform. Theory, 56, 4085 (2010)], shows that this conjecture holds when both matrices $A$ and $B$ are normal. In this paper, we prove that the conjecture holds when one of matrices $A$ and $B$ is normal and the other one is arbitrary. Our work makes solid progress towards this conjecture and thus the distillability problem.The pure entangled state is of vital importance in the field of quantum information. The process of asymptotically extracting pure entangled states from many copies of mixed states via local operations and classical communication is called entanglement distillation. The entanglement distillability problem, which is a long-standing open problem, asks whether such process exists. The 2-copy undistillability of $4\times4$ undistillable Werner states has been reduced to the validness of the a matrix inequality, that is, the sum of the squares of the largest two singular values of matrix $A\otimes I + I \otimes B$ does not exceed $(3d-4)/d^2$ with $A,B$ traceless $d\times d$ matrices and $||A||_F^2+||B||_F^2=1/d$ when $d=4$. The latest progress, made by Ł.~Pankowski~ et al~[IEEE Trans. Inform. Theory, 56, 4085 (2010)], shows that this conjecture holds when both matrices $A$ and $B$ are normal. In this paper, we prove that the conjecture holds when one of matrices $A$ and $B$ is normal and the other one is arbitrary. Our work makes solid progress towards this conjecture and thus the distillability problem.

arXiv:1908.02428Aug 7, 20191 citation

Disproving the Peres conjecture: nonlocality does not imply entanglement distillability

Tamás Vértesi, Nicolas Brunner

Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is however still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled. Then we show that this state nevertheless violates a Bell inequality. Our result also disproves the multipartite version of a longstanding conjecture made by Asher Peres.Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is however still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound entangled. Then we show that this state nevertheless violates a Bell inequality. Our result also disproves the multipartite version of a longstanding conjecture made by Asher Peres.

Jun 23, 20110 citations

Behaviour of quantum entanglement through incomparability

Amit Bhar

Jan 1, 20120 citations

4\times4

undistillable Werner states has been reduced to the validness of the a matrix inequality, that is, the sum of the squares of the largest two singular values of matrix

A\otimes I + I \otimes B

does not exceed

(3d-4)/d^2

with

A,B

traceless

d\times d

matrices and

||A||_F^2+||B||_F^2=1/d

when

d=4

. The latest progress, made by Ł.~Pankowski~ et al~[IEEE Trans. Inform. Theory, 56, 4085 (2010)], shows that this conjecture holds when both matrices

A

and

B

are normal. In this paper, we prove that the conjecture holds when one of matrices

A

and

B

is normal and the other one is arbitrary. Our work makes solid progress towards this conjecture and thus the distillability problem.